Problems with logaritm

Hello everyone! I have a few problem regarding Log.
First of all, it is a homework about Logarithm. I provide an image of my homework here:
(The ones squared with red are the ones I have problem with solving)
The main problem I have with Logs are the exponents. I know how to convert from logarithm form to exponent form and vice versa. But when solving for a variable exponent, it becomes difficult.
This is what I have done:
In problem 57.
I can solve a.
But b, c, and d are different.
In b. when solving on exponential form, how can I make a base with a variable exponent equal to a fraction (or decimal)?
In c. when solving on exponential form, how can I make a base with a variable exponent equal to a root?
The same goes with d.
In problem 58.
I could solve a. But it seems that b, c, and d, are solved differently. All of them contain negative exponents. How can I make a base with an exponent equal to another positive number if the exponent is negative?
Thanks in advance for the help!

Hello everyone! I have a few problem regarding Log.
First of all, it is a homework about Logarithm. I provide an image of my homework here:
...
(The ones squared with red are the ones I have problem with solving)
The main problem I have with Logs are the exponents. I know how to convert from logarithm form to exponent form and vice versa. But when solving for a variable exponent, it becomes difficult.
This is what I have done:
...

Hello everyone! I have a few problem regarding Log.
...
In problem 57.
I can solve a.
But b, c, and d are different.
In b. when solving on exponential form, how can I make a base with a variable exponent equal to a fraction (or decimal)?
In c. when solving on exponential form, how can I make a base with a variable exponent equal to a root?
The same goes with d.
In problem 58.
I could solve a. But it seems that b, c, and d, are solved differently. All of them contain negative exponents. How can I make a base with an exponent equal to another positive number if the exponent is negative?
Thanks in advance for the help!

If you have the equation

....... which you want to solve for x you only have to take both sides to the power